| I present the theory of elastic wave propagation in heterogeneous isotropic media and the Fourier method for their numerical simulation, where my original contributions are a new algorithm for a free boundary condition and the characterization of Fourier derivative operators with desirable sharp signatures.; I compare estimates of mid-ocean ridge magma lens width (700 m) from migrated seismic sections with the Fresnel zone diameter (∼1km) and show that the feature is seismically under resolved. Hence, magma properties, its liquid state, and lens thickness cannot be derived from the one dimensional methods used so far.; Through modeling I show that magma lenses continuous along the ridge axis for more than one Fresnel zone diameter would produce very strong converted PSP waves, otherwise absent in a large seismic data set collected in an area of significant volcanic activity at the East Pacific Rise. I propose that melts are concentrated in pockets smaller than the Fresnel zone diameter, interspersed in a body of melt-rich crystal mush. The continuity of the latter explains the continuity of seismic images, the discontinuity of the former explains the geochemical heterogeneity, superseding a long standing scientific conflict.; I propose a speculative model where melt pocket formation, crustal cracking and volcanic activity (diking and lava flow) are all simultaneously driven by magma migration and lithosphere extension imposed on a region of two contrasting rheologies: the brittle crust and the porous melt-percolated crystal mush. |
